The purpose of ICA is to separate a set of source signals from a set of mixed signals without requiring information about the source signals or the mixing process. ﻿

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﻿This concept can be more simply understood with the so-called cocktail-party problem, which deals with the difficult task of distinguishing between two original speech signals (i.e. two people talking independently of each other) when the signals are mixed together. Imagine that you are in a room where these two people are speaking simultaneously and being recorded by two microphones in different locations, with the microphones able to record time signals consisting of the amplitudes of the sound recordings and the time index. The goal of ICA, then, is to determine the original speech signals (see Figure 1 below) of the two people using only the mixed speech signals (see Figure 2 below) recorded by the two microphones.﻿

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﻿ICA works by assuming that the mixed signals are made up of additive subcomponents which are non-Gaussian signals and statistically independent from each other. In other words, each subcomponent is treated as a random variable rather than a proper time signal. ﻿

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﻿While ICA was originally developed to solve problems like the cocktail-party problem, it has since been found that the technique has many more applications than first anticipated. Some of these include:﻿

Separation of artifacts in magnetoencephalography (MEG) data: extracting the essential features of neuromagnetic signals in the presence of disruptive artifacts that may have higher amplitudes than the original brain signals and may resemble pathological signals in shape.

Finding hidden factors in financial data: trying to reveal common underlying factors in data about currency exchange rates or daily returns of stocks that would otherwise remain hidden.

Reducing noise in natural images: finding ICA filters for natural images and using the ICA decomposition to improve the clarity and sharpness of images that have been corrupted with additive Gaussiane noise.